Terahertz dielectric analysis and spin-phonon coupling in multiferroic ${\mathrm{GeV}}_4{\mathrm{S}}_8$

We present an investigation of the multiferroic lacunar spinel compound ${\mathrm{GeV}}_4{\mathrm{S}}_8$ using time-domain terahertz spectroscopy. We find three absorptions which either appear or shift at the antiferromagnetic transition temperature, $T_N=17\mathrm{K}$, as $S=1$ magnetic moments develop on vanadium tetrahedra. Two of these absorptions are coupled to the magnetic state and one only appears below the Néel temperature, and is interpreted as a magnon. We also observe isosbestic points in the dielectric constant in both the temperature and frequency domains. Further, we perform an analysis on the isosbestic features to reveal an interesting collapse into a single curve as a function of both frequency and temperature, behavior which exists throughout the phase transitions. This analysis suggests the importance of spectral changes in the terahertz range which are linear in frequency and temperature.

Figure 1

Susceptibility measured upon warming under a 500 Oe applied field. The inset represents the inverse susceptibility at low temperatures. The dashed lines in the inset show Curie-Weiss fits in the region above and below the structural transition.

Figure 2

The optical constants ${\sigma }_1$ and ${\varepsilon }_1$ are shown as a function of frequency [panels (a) and (b), respectively]. Temperature cuts are taken of this data for panels (c) and (d). An isosbestic point is observed at 1.04 THz in (b) and at $\sim 31.5\mathrm{K}$ in (d). Vertical dashed lines mark the isosbestic frequency in (a) and (b) and mark $T_N=17\mathrm{K}$ and $T_{JT}=31.5\mathrm{K}$ in (c) and (d). Arrows in ${\sigma }_1$ mark the absorptions. Only a subset of measured data are shown, in particular, ${\sigma }_1\left(\omega \right)$ at 32 K, just above $T_{JT}$, is marked in (a).

Figure 3

The temperature dependence of the width and center frequency of the 350 GHz phonon is shown in panel (a). The effects of spin-phonon coupling are clear in the changes of the behavior of the frequency of this mode at the magnetic ordering transition. Panel (b) shows the ratio ${\sigma }_1(T<30\text{K})/{\sigma }_1(T=30\text{K})$, which emphasizes the temperature behavior of the three observed absorptions. We have adjusted this ratio as described in the text to isolate the response of the absorptions from the background. The absorptions are seen to occur around 350 GHz, 600 GHz, and 1.2 THz, as indicated by arrows. The bump at 900 GHz is an artifact of the analysis and not a feature. Panel (c) shows the normalized spectral weight for the 520–720 GHz (, multiplied by 2) and 0.85–1.44 THz () regions and also the interpolated peaks from panel (b) $(▸$: 350 GHz absorption; $▸$: 1.2 THz absorption; error bars are from Gaussian fits to $\sim \pm 100$ GHz around each peak). The Néel temperature is marked by a vertical dashed line to emphasize the significance of the magnetic transition. Panel (d) shows selected fixed frequency cuts of panel (b). The emergence of the magnon is clearly seen below the Néel temperature marked as a vertical dashed line.

Figure 4

Optical constant data collapse after performing isosbestic analysis [24] on ${\tilde{\varepsilon }}_1$ in (a), and ${\widehat{\varepsilon }}_1$ in (b). The collapsed behavior of ${\tilde{\varepsilon }}_1(\omega ,T)$ is nearly constant and persists across the phase transitions. The low-temperature value has been subtracted from each ${\tilde{\varepsilon }}_1(\omega ,T)$ curve.

Figure 5

Gaussian fits in the region around the 350 GHz phonon in the imaginary part of the dielectric function. Fits are shown as a dashed black line, except for lowest temperature which is shown as a red dashed line for contrast. A representative selection of temperatures is shown from the full data set.